NON-COCOMMUTATIVE C*-BIALGEBRA DEFINED AS THE DIRECT SUM OF FREE GROUP C*-ALGEBRAS
نویسندگان
چکیده
منابع مشابه
C-bialgebra defined by the direct sum of Cuntz algebras
Katsunori Kawamura1 College of Science and Engineering Ritsumeikan University, 1-1-1 Noji Higashi, Kusatsu, Shiga 525-8577,Japan Abstract We show that there exists a non-cocommutative comultiplication ∆φ and a counit ε on the direct sum of Cuntz algebras O∗ ≡ C⊕O2 ⊕O3 ⊕O4 ⊕ · · · . From ∆φ, ε and the standard algebraic structure, the C ∗-algebra O∗ is a bialgebra. Furthermore we show the follow...
متن کامل7 C ∗ - bialgebra defined by the direct sum of Cuntz algebras ( The revised )
We show that a tensor product among representation of certain C∗-algebras induces a bialgebra. Let Õ∗ be the smallest unitization of the direct sum of Cuntz algebras O∗ ≡ C⊕O2 ⊕O3 ⊕O4 ⊕ · · · . We show that there exists a non-cocommutative comultiplication ∆ and a counit ε of Õ∗. From ∆, ε and the standard algebraic structure, Õ∗ is a C ∗-bialgebra. Furthermore we show the following: (i) The an...
متن کامل2 00 8 C ∗ - bialgebra defined by the direct sum of Cuntz - Krieger algebras
Let CK∗ denote the C ∗-algebra defined by the direct sum of all Cuntz-Krieger algebras. We introduce a comultiplication ∆φ and a counit ε on CK∗ such that ∆φ is a nondegenerate ∗-homomorphism from CK∗ to CK∗ ⊗ CK∗ and ε is a ∗-homomorphism from CK∗ to C. From this, CK∗ is a counital non-commutative non-cocommutative C ∗bialgebra. Furthermore, C∗-bialgebra automorphisms, a tensor product of repr...
متن کاملC-bialgebra defined by the direct sum of Cuntz-Krieger algebras
Let CK∗ denote the C ∗-algebra defined by the direct sum of all Cuntz-Krieger algebras. We introduce a comultiplication ∆φ and a counit ε on CK∗ such that ∆φ is a nondegenerate ∗-homomorphism from CK∗ to CK∗ ⊗ CK∗ and ε is a ∗-homomorphism from CK∗ to C. From this, CK∗ is a counital non-commutative non-cocommutative C ∗bialgebra. Furthermore, C∗-bialgebra automorphisms, a tensor product of repr...
متن کاملthe structure of lie derivations on c*-algebras
نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2015
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089515000099